On Fri, Nov 19, 1999 at 08:27:12PM -0800, Spike Jones wrote:
>The total number of posts
>I receive each day is far more predictable than the number
>of posts on GIMPS. Predictably.
Funnily enough, when I receive nothing from GIMPS, I receive nothing
from other people either! (No, this is not a mail burp. I still receive
_some_ mail.)
To get you something to do, here's an interesting problem. The beaty
if it, is that you could do it by brute-force, or you could simply
look at it, or see a solution and solve it in under a minute. Pen and
paper allowed only -- no calculators, computers etc.
First, perhaps I should explain some notation :-) a_11 is the letter `a',
followed by 11 in subscript. x^2 is the letter `x', followed by the letter
2 in superscript (ie. `x^2' would be mathematically the same as `x*x').
OK, here goes:
If (3x^2 - x - 2)^6 = (a_12)x^12 + (a_11)x^11 + ... + (a_1)x + a_0, what
is a_0 + a_2 + a_4 + ... + a_12?
The answer is an integer from 0 to 999, inclusive.
(This is just one of the problems from something called the `Abel
contest', a voluntary contest in maths open to all pupils (<21, but in
general nobody under 18 enters) in Norway. They have a tradition of
making problems requiring very little actual mathematical knowledge
(generally if you know (a+b)^2 = a^2 + 2ab + b^2 and Pythagoras, you
have 90% of what you need), but more requiring the right way of thinking.
Also, only pen and paper is used, to prevent some ways of solving the
problems... This question was number 9 (of 10), from the second round,
where the contestants (the 10% best from round one) are given 100
minutes to try to solve the 10 questions.)
Hope most of you see the quick solution :-) Please don't post the answer
to the list quite yet, give people their time...
/* Steinar */
--
Homepage: http://members.xoom.com/sneeze/
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